In a 6- to 8-quart pan over high heat, bring chicken, broth, and whole sage leaves to a boil. Reduce heat to low, cover, and simmer, skimming off and discarding any foam that rises to the surface, until chicken is no longer pink at bone (cut to test), about 30 minutes.
Meanwhile, cut off and discard root ends and dark green tops from leeks. Cut white and pale green parts in half lengthwise and rinse well under running water, flipping layers to release grit. Thinly slice leeks crosswise.
Lift chicken from broth. When cool enough to handle, pull meat into shreds (discard bones).
Add potatoes, celery, carrots, leeks, and 2 cups water to pan with broth. Bring to a boil over high heat, then reduce heat to medium, cover, and simmer until vegetables are tender when pierced, 20 to 30 minutes. Stir in shredded chicken.
Meanwhile, in a large bowl, mix flour, cornmeal, baking powder, salt, and the chopped sage. Stir in milk, beaten egg and egg white, and the melted butter just until combined.
Drop dumpling batter in 12 to 14 heaping tablespoon portions on the surface of the simmering soup. Cover pan and simmer over medium-low heat (do not allow soup to boil) until a knife inserted into the center of a dumpling comes out clean, about 10 minutes. Ladle hot soup into bowls.